But I think it has more to do with the Fed trying to appease both the political party in power (as they control their renomination) and just people generally.

With all the social media etc nowadays, they have more scrutiny over their actions, and are afraid of making tough decisions. E.g. optimizing for the short run to the expense of the longer run.

But to your point, Powell in particular is much more focused on the stock market and how wealthier Americans (stockholders, homeowners etc) are doing. Past fed chairmen, like Yellen and Bernanke didn't seem to care nearly as much about market movements, and focused more on the economy itself, and their mandate.